Pith Number

pith:3M6A4ODO

pith:2011:3M6A4ODOCK7LF4ZZ2VN2XITF7Q

not attested not anchored not stored refs pending

Structure of fundamental groups of manifolds with Ricci curvature bounded below

Burkhard Wilking, Vitali Kapovitch

arxiv:1105.5955 v2 · 2011-05-30 · math.DG · math.GT

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3M6A4ODOCK7LF4ZZ2VN2XITF7Q}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

4 papers in Pith

A Large-Diameter Fundamental-Gap Lower Bound for Horoconvex Domains

Nonnegative Ricci curvature and virtual abelianness in dimensions less than 12

Structure of Torus Fibration Under the First Betti Number Restriction

Complete manifolds with nonnegative Ricci curvature and slow relative volume growth

Receipt and verification

First computed	2026-05-18T04:09:45.708521Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db3c0e386e12beb2f339d55baba265fc264cc489a8557369bdcd97c8a756b08d

Aliases

arxiv: 1105.5955 · arxiv_version: 1105.5955v2 · doi: 10.48550/arxiv.1105.5955 · pith_short_12: 3M6A4ODOCK7L · pith_short_16: 3M6A4ODOCK7LF4ZZ · pith_short_8: 3M6A4ODO

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3M6A4ODOCK7LF4ZZ2VN2XITF7Q \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: db3c0e386e12beb2f339d55baba265fc264cc489a8557369bdcd97c8a756b08d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2036b0afb0d4b32d02a357966859b776dd7c4dc9d4ed3636b22d5e1a3060e6fe",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DG",
    "submitted_at": "2011-05-30T12:18:55Z",
    "title_canon_sha256": "04041b790da5dd231d08d3638e3d5acc02c964cf3453f2a282770b4a5b9cf551"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.5955",
    "kind": "arxiv",
    "version": 2
  }
}